U.S. President Donald Trump said Wednesday that he received a "great letter" from North Korean leader Kim Jong-un and expects the two will have another meeting soon.

Kim said in his New Year's address Tuesday that he is ready for a second meeting with Trump at any time and is committed to "complete denuclearization."

But he also warned that the North may be compelled to "find a new way" to defend its interests if the U.S. continues with sanctions and pressure against the regime.

"I just got a great letter from Kim Jong-un," Trump told reporters at a Cabinet meeting at the White House, according to news reports. "We'll probably have another meeting."

It wasn't clear when the U.S. president had received the letter. A South Korean newspaper earlier reported that a message was delivered last Friday.

The two leaders exchanged a series of letters -- some made public -- in the wake of Kim's offer early last year to meet Trump and resolve heightened tensions caused by the North's nuclear weapons and ballistic missile tests in 2017.

They held their first summit in Singapore in June and agreed to "work toward" complete denuclearization of the Korean Peninsula in exchange for security guarantees from the U.S.

Trump said Wednesday there would be a "big fat war in Asia" had the two not met.

Progress on implementing the summit agreement has stalled, with the North demanding sanctions relief and the U.S. insisting on more concrete steps to dismantle the regime's nuclear program.

Still, Trump said last month that he expected a second summit in January or February.

And in response to Kim's speech Tuesday, he tweeted: "I also look forward to meeting with Chairman Kim who realizes so well that North Korea possesses great economic potential!" (Yonhap)